Solve Propertiesstraightline G(x)=5x-12x2 Tiger Algebra Solver

Reformatting the input :

Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : g*(x)-(5*x-12*x^2)=0

Step 1 :

Equation at the end of step 1 :

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors : gx + 12x2 - 5x = x • (g + 12x - 5)

Equation at the end of step 3 :

Step 4 :

Theory - Roots of a product :

4.1 A product of several terms equals zero.When a product of two or more terms equals zero, then at least one of the terms must be zero.We shall now solve each term = 0 separatelyIn other words, we are going to solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

4.2 Solve : x = 0 Solution is x = 0

Equation of a Straight Line

4.3 Solve g+12x-5 = 0 Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK). "y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.In this formula :y tells us how far up the line goesx tells us how far alongm is the Slope or Gradient i.e. how steep the line isb is the Y-intercept i.e. where the line crosses the Y axisThe X and Y intercepts and the Slope are called the line properties. We shall now graph the line g+12x-5 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of g is 5/1 so this line "cuts" the g axis at g= 5.00000

Calculate the X-Intercept :

When g = 0 the value of x is 5/12 Our line therefore "cuts" the x axis at x= 0.41667

Calculate the Slope :

Slope is defined as the change in g divided by the change in x. We note that for x=0, the value of g is 5.000 and for x=2.000, the value of g is -19.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -19.000 - 5.000 = -24.000 in g. (The change in g is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Geometric figure: Straight Line

1. Slope = -24.000/2.000 = -12.000
2. x-intercept = 5/12 = 0.41667
3. g-intercept = 5/1 = 5.00000
4. x = 0